Question

6 select the mean, median, mode and range for the following list of values. 13, 18, 13, 14, 13, 16, 14, 21, 13
averages \t14 \t15 \t13
mean \t□ \t□ \t□
median \t□ \t□ \t□
mode \t□ \t□ \t□

Explanation:

Step1: Calculate the Mean

First, sum all the values: \(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13\). Let's compute that: \(13\times4 + 14\times2 + 16 + 18 + 21 = 52 + 28 + 16 + 18 + 21 = 135\). There are 9 values, so the mean is \(\frac{135}{9}=15\).

Step2: Calculate the Median

First, order the data: \(13, 13, 13, 13, 14, 14, 16, 18, 21\). There are 9 values (odd number), so the median is the middle value, which is the 5th value. The 5th value is \(14\).

Step3: Calculate the Mode

The mode is the value that appears most frequently. \(13\) appears 4 times, which is more than any other value, so the mode is \(13\).

Step4: Calculate the Range (though not in the table, but for clarity)

Range is maximum - minimum. Maximum is \(21\), minimum is \(13\), so range is \(21 - 13 = 8\), but we focus on mean, median, mode here.

Now, filling the table:

• Mean: 15 (so check the box under 15 for Mean)
• Median: 14 (so check the box under 14 for Median)
• Mode: 13 (so check the box under 13 for Mode)

Answer:

• Mean: \(\boldsymbol{15}\) (check the box under 15 in the Mean row)
• Median: \(\boldsymbol{14}\) (check the box under 14 in the Median row)
• Mode: \(\boldsymbol{13}\) (check the box under 13 in the Mode row)